We report the independent discovery and follow-up observations of supernova 2005gj by the Nearby Supernova Factory . This is the second confirmed case of a “ hybrid ” Type Ia/IIn supernova , which like the prototype SN 2002ic , we interpret as the explosion of a white dwarf interacting with a circumstellar medium . Our early-phase photometry of SN 2005gj shows that the strength of the interaction between the supernova ejecta and circumstellar material is much stronger than for SN 2002ic . Our first spectrum shows a hot continuum with broad and narrow H \alpha emission . Later spectra , spanning over 4 months from outburst , show clear Type Ia features combined with broad and narrow H \gamma , H \beta , H \alpha and He i \lambda \lambda 5876,7065 in emission . At higher resolution , P Cygni profiles are apparent . Surprisingly , we also observe an inverted P Cygni profile for [ O iii ] \lambda 5007 . We find that the lightcurve and measured velocity of the unshocked circumstellar material imply mass loss as recently as 8 years ago . This is in contrast to SN 2002ic , for which an inner cavity in the circumstellar material was inferred . Within the context of the thin-shell approximation , the early lightcurve is well-described by a flat radial density profile for the circumstellar material . However , our decomposition of the spectra into Type Ia and shock emission components allows for little obscuration of the supernova , suggesting an aspherical or clumpy distribution for the circumstellar material . We suggest that the emission line velocity profiles arise from electron scattering rather than the kinematics of the shock . This is supported by the inferred high densities , and the lack of evidence for evolution in the line widths . Ground- and space-based photometry , and Keck spectroscopy , of the host galaxy are used to ascertain that the host galaxy has low metallicity ( Z / Z _ { \odot } < 0.3 ; 95 % confidence ) and that this galaxy is undergoing a significant star formation event that began roughly 200 \pm 70 Myr ago . We discuss the implications of these observations for progenitor models and cosmology using Type Ia supernovae .